audiophiles have long insisted on turning the speakers off (that is, turning the volume all the way down)
before turning the amplifier on or off.
the reason is that you could turn the amplifier on and blast the speakers with an amplifier transient
consider a big machine that moves stuff
if you turn that on before the control system, you have no idea what its going to do
each time you turn it on, without the control system on, it could respond differently
power up and power down includes the peripherals and it includes the control circuits
turn on the processor first so its outputs can settle to OFF
this also allows the inputs to be known when things start up
then turn on the sensor power so the sensors are up and running
then turn on the controlled machines
what is your ECU, and what are you controlling, so you may get a more specific answer?